Module 12 Test Review: Radical Expressions and Equations

Name _______________________________________ Date __________________ Class __________________

Module 12 Test Review: Radical Expressions and Equations

For 1?3, translate the expression with rational exponents into a radical expression and simplify, if possible.

7

1. y 4

_______________________________________

2

2.

243 32

5

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3. (81)0.75

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4. Is each expression equivalent to 0.361.5 ?

2

A 0.363

Yes

No

B 0.216

Yes

No

2

C 3 0.36

Yes

No

8. 5 323

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9. The annual rate of inflation, in percent, of

a home that increases in value from p to

q over a period of n years is

1

I

100

q p

n

100.

Find

the

annual

rate

of inflation, to the nearest tenth of a

percent, of a home that doubles in value

over 20 years.

________________________________________

10. Is each expression equivalent to n s ? t

1

A sn 1 tn

B

1

-1

Yes

No

Yes

No

3

D 0.362

E 0.363

Yes

No

Yes

No

C ns nt

D n s n t

Yes

No

Yes

No

For 5?8, translate the radical expression into an expression with rational exponents and simplify, if possible.

1

E

s n t

Yes

No

5. m9

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6. 6 4 3

_______________________________________

7. 3 85

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For 11?16, simplify the expression. Assume that all variables are positive. All exponents should be positive in simplified form. Rationalize any irrational denominators.

3

5 4

11.

83

7

89

________________________________________

Original content Copyright ? by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.

59

Name _______________________________________ Date __________________ Class __________________

2 2

12.

5a3 b

7

6b 5

_______________________________________

x5y3 13.

4 x2y5

19. 3x 13 x 5

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20. 3 4x 1 5

________________________________________

21. 3x 11 x 3

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14. 5 325 61252

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15. 3 21m2 3 7m2n

_______________________________________ 34 380

16. 35

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17. The surface area S of a sphere as a

function of its volume V is given by

2

S

4

3V 4

3

.

Rewrite

the

expression

for

the surface area as the product of a

simplified coefficient term and a variable

term using only positive exponents. Then

write the approximate formula with the

coefficient term rounded to the nearest

thousandth.

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For 18?22, solve each equation. Identify any extraneous roots.

1

18. x 32 1 x

_______________________________________

________________________________________

1

22. 2 x 23 x 2

________________________________________

23. Choose True or False for each statement

1

about the equation x 142 x 2.

A It has one solution.

True

False

B It has two solutions.

True

False

C It has one extraneous solution.

True

False

D It has two extraneous solutions.

True

False

E It has no solutions.

True

False

24. The equation + 6400 = 31.3 ? 1011 2 relates the distance d in kilometers of a certain GPS satellite above the surface of the Earth to the number of hours t it takes the satellite to complete one orbit. The average distance of this satellite above the surface of the Earth is 20,100 kilometers. To the nearest hour, how long does it take the GPS satellite to complete one orbit of the Earth?

_________________________________

Original content Copyright ? by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.

60

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